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<span class="kw">let </span><font color="Maroon" title="c1">GF</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">GF</font><br/> for <font color="Olive" title="b2">W</font> being   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b1">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  holds <br/><font color="Olive" title="b2">W</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">GF</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>  st <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  holds <br/><font color="Olive" title="b1">W</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">W</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  implies <font color="Maroon" title="c3">W</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  )</span><br/>





<span class="kw">consider </span><font color="Maroon" title="c4">A</font> being    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c3">W</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">I</font> being    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E3:31"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_9.html#T17" target="_self" title="VECTSP_9:th.17">Th17</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:31"/>
<font color="Maroon" title="c2">V</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">W</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> </span><br/>

<a NAME="E5:31"/><span class="kw">then </span>
<font color="Maroon" title="c5">I</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_9.html#T24" target="_self" title="VECTSP_9:th.24">Th24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:31"/>
<font color="Maroon" title="c3">W</font> is  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:31"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="matrlin.html#D3" title="MATRLIN:def.3">MATRLIN:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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